SME
Grade 7 Math · Problem type
p(x + q) = r
Use this for “4 boxes, 12 pens given away from each, 100 left: how many were in a box?”
Diagram
4(x − 12) = 100
4 × (37 − 12) = 4 × 25 = 100
This is an example. Type your own values to start a new problem.
p
(x
+
(
q
)
)
=
r
x
Unknown
calculated
Formulas
p
×
(
x
+
q
)
=
r
(groups
×
(unknown
+
added
to
each)
=
total)
4 × (37 + (−12)) = 100
Assumptions
•
The bar is p equal groups, each x and q, together as long as r.
•
A negative q takes from each group: q = −12 makes each group x − 12.
•
Divide by p first for one group, or multiply out first: both work.
Step-by-step
WE KNOW
p = 4 (groups), q = −12 (added to each), r = 100 (total)
FIND
unknown (x)
Step 1 · Find unknown (x)
Use p × (x + q) = r (groups × (unknown + added to each) = total)
Divide
both
sides
by
p
,
then
take
q
from
both
sides.
4(
x
−
12)
=
100
Divide
both
sides
by
4:
x
−
12
=
25
Add
12
to
both
sides:
x
=
25
+
12
x
=
37
Check
Put the numbers back in. Both sides should match.
4 × (37 − 12) = 100 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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